The HIFI instrument on board the Herschel Space Observatory has been used to observe interstellar nitrogen hydrides along the sight-line towards G10.6-0.4 in order to improve our understanding of the interstellar chemistry of nitrogen. We report observations of absorption in NH N=1-0, J=2-1 and ortho-NH2 1_1,1-0_0,0. We also observed ortho-NH3 1_0-0_0, and 2_0-1_0, para-NH3 2_1-1_1, and searched unsuccessfully for NH+. All detections show emission and absorption associated directly with the hot-core source itself as well as absorption by foreground material over a wide range of velocities. All spectra show similar, non-saturated, absorption features, which we attribute to diffuse molecular gas. Total column densities over the velocity range 11-54 km/s are estimated. The similar profiles suggest fairly uniform abundances relative to hydrogen, approximately 6*10^-9, 3*10^-9, and 3*10^-9 for NH, NH2, and NH3, respectively. These abundances are discussed with reference to models of gas-phase and surface chemistry.